ADC Quantization Noise Voltage
e = (FS / 2ᴺ) / √12
Quick answer
This calculator solves e(rms) = q / √12, q = FS / 2ᴺ for RMS Quantization Noise. With Full-Scale Range 12 V, Resolution (bits) 0.5, the result is 2.449 V. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Rounding a continuous signal to discrete ADC codes introduces quantization error spread over one least-significant-bit step (q). Treated as uniform noise, its RMS value is the LSB size divided by √12. This is the fundamental noise floor of an ideal converter and the basis from which the familiar SNR = 6.02N + 1.76 dB result is derived.
Variables
- e — RMS quantization noise voltage (V)
- FS — Full-scale input range (V)
- N — Resolution in bits
Practical Notes
The LSB voltage is q = FS/2ᴺ. Real converters add thermal and jitter noise on top, so their effective resolution (ENOB) is below N.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| e | RMS Quantization Noise | µV | pV, nV, µV, mV, V, kV |
| FS | Full-Scale Range | V | pV, nV, µV, mV, V, kV |
| N | Resolution (bits) | — | — |
Step by step
- 1. What you know: Full-Scale Range 12 V, Resolution (bits) 0.5
- 2. The relation: e(rms) = q / √12, q = FS / 2ᴺ
- 3. Substitute: FS = 12 V, N = 0.5
- 4. Result: RMS Quantization Noise = 2.449 V
Worked examples
Minimum range
Given: Full-Scale Range 0.33 V, Resolution (bits) 0.025
Result: RMS Quantization Noise = 93.63 mV
Low range
Given: Full-Scale Range 3.3 V, Resolution (bits) 0.25
Result: RMS Quantization Noise = 0.8011 V
Typical
Given: Full-Scale Range 12 V, Resolution (bits) 0.5
Result: RMS Quantization Noise = 2.449 V
High range
Given: Full-Scale Range 0.23 kV, Resolution (bits) 0.8
Result: RMS Quantization Noise = 38.13 V
Maximum range
Given: Full-Scale Range 2.3 kV, Resolution (bits) 8
Result: RMS Quantization Noise = 2.594 V
Solving for each variable
Solve for RMS Quantization Noise
Full-Scale Range 0.33 V, Resolution (bits) 0.025 → 93.63 mV
Solve for Full-Scale Range
RMS Quantization Noise 1 µV, Resolution (bits) 0.025 → 3.525 µV
How RMS Quantization Noise changes with Full-Scale Range
| Full-Scale Range (input) | RMS Quantization Noise (result) |
|---|---|
| 1.2 V | 0.2449 V |
| 3 V | 0.6124 V |
| 6 V | 1.225 V |
| 9 V | 1.837 V |
| 12 V | 2.449 V |
| 18 V | 3.674 V |
| 24 V | 4.899 V |
| 48 V | 9.798 V |
| 84 V | 17.15 V |
| 120 V | 24.49 V |
The same result in other units
| Unit | Value |
|---|---|
| µV | 2449000 |
| mV | 2449 |
| V | 2.449 |
| kV | 0.002449 |
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<p><a href="https://vbatpower.com/formulas/quantization-noise-voltage/">ADC Quantization Noise Voltage</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate ADC Quantization Noise Voltage?
Use e(rms) = q / √12, q = FS / 2ᴺ. With Full-Scale Range 12 V, Resolution (bits) 0.5, RMS Quantization Noise works out to 2.449 V.
What is the formula for ADC Quantization Noise Voltage?
The formula is e(rms) = q / √12, q = FS / 2ᴺ. Rounding a continuous signal to discrete ADC codes introduces quantization error spread over one least-significant-bit step (q).
How do you find Full-Scale Range when you know the other values?
Rearrange for Full-Scale Range: with RMS Quantization Noise 1 µV, Resolution (bits) 0.025, Full-Scale Range is 3.525 µV.
What units does ADC Quantization Noise Voltage use?
RMS Quantization Noise is shown in µV, mV, V, kV. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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